Quantum Criticality in the 2D Quasiperiodic Potts Model.

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equationconjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

The N-color quantum Ashkin–Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin–Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers N, and the critical behavior for all . In the case of two colors, N = 2, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all , i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman–Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.

The electromagnetic response of topological insulators and superconductors is governed by a modified set of Maxwell equations that derive from a topological Chern-Simons (CS) term in the effective Lagrangian with coupling constant $\kappa$. Here we consider a topological superconductor or, equivalently, an Abelian Higgs model in $2+1$ dimensions with a global $O(2N)$ symmetry in the presence of a CS term, but without a Maxwell term. At large $\kappa$, the gauge field decouples from the complex scalar field, leading to a quantum critical behavior in the $O(2N)$ universality class. When the Higgs field is massive, the universality class is still governed by the $O(2N)$ fixed point. However, we show that the massless theory belongs to a completely different universality class, exhibiting an exotic critical behavior beyond the Landau-Ginzburg-Wilson paradigm. For finite $\kappa$ above a certain critical value $\kappa_c$, a quantum critical behavior with continuously varying critical exponents arises. However, as a function $\kappa$ a transition takes place for $|\kappa| < \kappa_c$ where conformality is lost. Strongly modified scaling relations ensue. For instance, in the case where $\kappa^2>\kappa_c^2$, leading to the existence of a conformal fixed point, critical exponents are a function of $\kappa$.

Optical properties of NdAg in the ferromagnetic and paramagnetic phases

Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii–Kosterlitz–Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

We propose generalized variants of the XY model capable of exhibiting an arbitrary number of phase transitions only by varying temperature. They are constructed by supplementing the magnetic coupling with n_{t}-1 nematic terms of exponentially increasing order with the base q=2,3,4, and 5, and increasing interaction strength. It is found that for q=2,3, and 4 with sufficiently large coupling strength of the final term, the models exhibit a number of phase transitions equal to the number of the terms in the generalized Hamiltonian. Starting from the paramagnetic phase, the system transitions through the cascade of n_{t}-1 nematic phases of the orders q^{k},k=n_{t}-1,n_{t}-2,⋯,1, that are characterized by q^{k} preferential spin directions symmetrically disposed around the circle, to the ferromagnetic (FM) phase at the lowest temperatures. Besides the Berezinskii-Kosterlitz-Thouless (BKT) transition from the paramagnetic phase, all the remaining transitions have a non-BKT nature: depending on the value of q they belong to either the Ising (q=2 and 4) or the three-state Potts (q=3) universality class. For q=5, due to the interplay between different terms, the phase transitions between the ordered phases observed for q<5 split into two, and the number of the ordered phases increases to 2n_{t}-1. These phases are characterized by a domain structure with the gradually increasing short-range FM ordering within domains that extends to different kinds of FM ordering in the last two low-temperature phases. The respective transitions do not seem to obey any universality.

We investigate the non-equilibrium stationary states of the Ising, X Y , and Heisenberg models on a simple cubic lattice using Monte Carlo simulations. The system’s evolution is governed by a competition between two dynamics controlled by a parameter q : a one-spin flip dynamic that drives the system, in contact with a thermal reservoir at temperature T , towards a lower energy state with probability q , and a two-spin flip dynamic that drives it, subjected to an external energy flux, towards a higher energy state with probability 1 − q . We construct the phase diagram of T as a function of q , which exhibits a rich phenomenology of self-organization across the different observed phases and is characterized by continuous phase transitions between them. For all three models, we identify three distinct phases: an antiferromagnetic ordered phase at low q values, a disordered paramagnetic phase at intermediate q , and a ferromagnetic ordered phase at high q values and low T . Furthermore, we calculate the critical exponents for the phase transitions and show that they remain unchanged from their equilibrium values, indicating that the non-equilibrium nature of the dynamics does not alter the universality class of the models. This suggests that the underlying symmetries of the models are the primary determinants of their critical behavior, even in the presence of a persistent energy flux. • We study Ising, XY, and Heisenberg models under competing stochastic dynamics. • Self-organized antiferromagnetic, paramagnetic, and ferromagnetic phases emerge. • Critical exponents match equilibrium values despite detailed balance violation. • Universality classes are preserved in non-equilibrium driven magnetic systems.

We propose families of infinitely ramified fractals, which we call the m-sheet Sierpinski gasket with side b [(mSG${)}_{\mathit{b}}$], on which the q-state Potts model can be exactly solvable through a real-space renormalization-group (RSRG) technique for which there are phase transitions at finite temperatures for m&gt;1. We also propose, within a cell-to-cell RSRG scheme, a criterion for a suitable choice of cells in the study of antiferromagnetic (AF) classical spin models defined on (or approximated by) multirooted hierarchical lattices, and apply it for the AF Potts model on some (mSG${)}_{\mathit{b}}$ fractals. Concerning the Ising model on the (mSG${)}_{2}$ family, we obtain the exact para (P)--ferromagnetic (F) critical temperature as a function of m and verify that, for m=1 and 2, there is no AF order (not even at zero temperature). We calculated the exact P-F and possibly exact P-AF critical frontiers and the corresponding correlation-length critical exponents for q=2-, 3-, and 4-state Potts model on the (mSG${)}_{4}$. The AF q=2 and 4 cases have highly degenerate ground states and each one presents, above a certain critical fractal dimension ${\mathit{D}}_{\mathit{f}}^{\mathit{c}}$(q,m), an unusual low-temperature phase whose attractor occurs at a non-null temperature. For q=2 and ${\mathit{D}}_{\mathit{f}}$(2,m)\ensuremath{\ge}5.1, we prove that the correlations have a power-law decay with distance along this entire phase.

Quantum phase transitions and quantum critical behavior can be observed in magnetically unstable 4f- and 3d-electron systems. In contrast to classical phase transitions, which are induced by temperature changes, quantum phase transitions arise as a result of the variation of a non-thermal control parameter. A great number of complex magnetic ground states are observed close to such quantum phase transitions, which are not fully understood yet. Therefore, we performed stoichiometry studies of CePt3B1-xSix, Nb1-yFe2+y and Ta(Fe1-xVx)2. During the determination of the magnetic ground state properties of the observed materials studies were performed on a macroscopic scale by measurements of magnetization, resistivity and specific heat and on a microscopic scale by muon spin rotation (µSR) and 57Fe Mossbauer spectroscopy. Combining these different experimental methods has led to comprehensive insights into the static and dynamic magnetic properties and allows the construction of magnetic phase diagrams. For low silicon concentration, the non-centrosymmetric system CePt3B1-xSix shows physical properties similar to those of CePt3B: an antiferromagnetic ground state and for lower temperatures a weakly ferromagnetic phase. Increasing silicon content leads to a continuous decrease of the antiferromagnetic phase, while the weakly ferromagnetic ordering is completely suppressed for a critical Si concentration. Further, the heavy-fermion system CePt3Si exhibits an additional unconventional superconducting phase. Moreover, the magnetic ground state properties of the isostructural C14 Laves phase systems Nb1-yFe2+y and Ta(Fe1-xVx)2 are investigated in this thesis. Slight changes in stoichiometry lead to complex magnetic phase diagrams in both systems, with evidence for quantum critical behavior at the transition from a ferromagnetic ordering to a spin density wave (SDW) ordering. Detailed µSR experiments confirm the rare case of a SDW modulated phase in Nb1-yFe2+y, which is surrounded by ferromagnetic phases and a quantum critical point. Furthermore, the magnetic properties exhibit quantum critical behavior for critical concentrations. 57Fe Mossbauer spectroscopy also identified Ta(Fe1-xVx)2 as a system with a SDW modulated phase. Further, a ferromagnetic instability for x = 0.02 in Ta(Fe1-xVx)2 is observed by means of magnetization studies. This indicates a quantum critical behavior similar to the behavior of Nb1-yFe2+y.

Magnetic, electronic, and thermal transport properties of ${\mathrm{Eu}}_{0.55}{\mathrm{Sr}}_{0.45}\mathrm{Mn}{\mathrm{O}}_{3}$ have been experimentally studied. The compound is found to exhibit a complex magnetic behavior with the change of temperature and magnetic field. Without magnetic field, it stays in a Griffiths-like state in a wide temperature range above $\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, characterized by the presence of ferromagnetic (FM) clusters of the size of $\ensuremath{\sim}8$ Mn ions, and an antiferromagnetic (AFM) state below $\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, evidenced by thermopower and heat conductivity. FM phase emerges and grows in the AFM matrix with applied field, resulting in a series of phase transitions from the paramagnetic (PM) state first to the AFM state, then to the FM and the AFM states upon cooling $(\ensuremath{\sim}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{T}lHl\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{T})$, or a simple PM-FM transition $(Hg\ensuremath{\sim}2.3\phantom{\rule{0.3em}{0ex}}\mathrm{T})$. The AFM state is unstable under high fields, and the high- and low-temperature AFM transitions are depressed by the fields above $\ensuremath{\sim}1$ and $\ensuremath{\sim}2.3\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, respectively. The FM transition is incomplete when the field is below $\ensuremath{\sim}1.5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, leading to a coexistence of the FM and PM (or AFM) phases in the intermediate temperature range. A spin-glass-like behavior is observed in the AFM background below $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Significant response of resistance, thermopower, and heat conduction to magnetic transition, either FM or AFM transition, has been observed. Unlike the typical AFM manganites, for which usually a depression of thermal conduction occurs at the AFM state, the AFM transition in ${\mathrm{Eu}}_{0.55}{\mathrm{Sr}}_{0.45}\mathrm{Mn}{\mathrm{O}}_{3}$ enhances the thermal conduction. From the PM phase to the AFM phase and to the FM phase, thermal conductivity increases monotonically. A remarkable result of the present work is the different behaviors of thermopower and resistivity. The former displays a metallic behavior below a distinct temperature that is significantly lower than the metal-to-insulator transition temperature determined by resistivity. Furthermore, thermopower remains metallic while the resistivity shows up an upturn due to the AFM transition in the low-temperature range under the field of $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Based on these data, a magnetic phase diagram is proposed.

The quantum criticality and entanglement properties are investigated in the one-dimensional spin-1/2 transverse field Ising model with staggered Dzyaloshinskii–Moriya interaction by utilizing the infinite-time evolving block decimation method. In this model, the staggered Dzyaloshinskii–Moriya interaction does not lead any new phase, while it only appears a phase transition line between Néel phase and paramagnetic phase. The behaviors of measurements of information illustrate the quantum phase transition and the existence of factorized points. The factorization phenomena is observed in the transverse Néel phase detecting by the entanglement quantities, in which the double degenerate ground state in transverse Néel phase is preserved by the Dzyaloshinskii–Moriya interaction also evidencing from the fidelity map. From the perspective of magnetism, the existence of chiral order and transverse Néel order suggests the helical magnetic structure induced by Dzyaloshinskii–Moriya interaction. The critical exponents and central charge keep invariant and convinced that the phase transitions belong to the Ising universality class. In contrary to the systems confined within central charge c=1, although the competition between the Dzyaloshinskii–Moriya interaction and external field changes the phase transition and entanglement properties, the quantum criticality seems independent of Dzyaloshinskii–Moriya interaction.

We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter . The model was studied by Law et al (2010 Phys. Rev. B 81 041305(R)), and was mapped onto an anisotropic two-channel Kondo model via bosonization. For , the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between the dot and the 2DTI based on a simple scaling dimensional analysis (Law et al 2010 Phys. Rev. B 81 041305(R). We re-examine this model beyond the bare scaling dimension analysis via a one-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for a fixed value of that the 2CK fixed point can be unstable towards the 1CK fixed point and the system is expected to undergo a quantum phase transition between 1CK and 2CK fixed points with changing Kondo couplings. Our RG approach is controlled near K = 1. In general, this QPT can also occur upon tuning the Luttinger parameter K to a critical value smaller than unity () for fixed Konodo couplings. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for .

We consider quantum quench by a time dependent double trace coupling in a strongly coupled large N field theory which has a gravity dual via the AdS/CFT correspondence. The bulk theory contains a self coupled neutral scalar field coupled to gravity with negative cosmological constant. We study the scalar dynamics in the probe approximation in two backgrounds: AdS soliton and AdS black brane. In either case we find that in equilibrium there is a critical phase transition at a {\em negative} value of the double trace coupling $\kappa$ below which the scalar condenses. For a slowly varying homogeneous time dependent coupling crossing the critical point, we show that the dynamics in the critical region is dominated by a single mode of the bulk field. This mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads to Kibble Zurek type scaling behavior. For the AdS soliton the system is non-dissipative and has $z=1$, while for the black brane one has dissipative $z=2$ dynamics. We also discuss the features of a holographic model which would describe the non-equilibrium dynamics around quantum critical points with arbitrary dynamical critical exponent $z$ and correlation length exponent $\nu$. These analytical results are supported by direct numerical solutions.

Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic N\'eel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends is gapless, while the surface exposed along the ladders is gapful, in the Haldane phase. Conversely, in the gapped rung singlet phase, the former surface is gapped, and the latter is gapless. We demonstrate that, although mechanisms of the two gapless modes are different, nonordinary surface critical behaviors are realized at both critical points on the gapless surfaces exposed by simply cutting bonds without fine-tuning the surface coupling required to reach a multicritical point in classical models. We also show that, on the gapped surfaces, the surface critical behaviors are in the ordinary class.

We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different sets of critical exponents, but having a common transition temperature. We solve this problem analytically in the frame of ${\ensuremath{\phi}}^{k}$ mean-field theory, which is then generalized using phenomenological scaling considerations. A large variety of interface critical behavior is obtained which is checked numerically on the example of two-dimensional $q$-state Potts models with $2\ensuremath{\leqslant}q\ensuremath{\leqslant}4$. Weak interface couplings are generally irrelevant, resulting in the same critical behavior at the interface as for a free surface. With strong interface couplings, the interface remains ordered at the bulk transition temperature. More interesting is the intermediate situation, the special interface transition, when the critical behavior at the interface involves new critical exponents, which, however, can be expressed in terms of the bulk and surface exponents of the two subsystems. We discuss also the smooth or discontinuous nature of the order parameter profile.